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MultiWay Conventional loudspeakers with crossovers 

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26th May 2004, 02:50 PM  #1 
diyAudio Member
Join Date: Aug 2003
Location: Quebec city

SPL function of speed or acceleration
Hello Mathematicians out there.
Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone. F 
26th May 2004, 03:38 PM  #2 
diyAudio Member
Join Date: Aug 2002
Location: Seattle or Shanghai

Acceleration of the cone. This is why the velocity doubles as you drop an octave, and the displacement quadruples as you drop an octave (assuming the SPL level stays the same).
Dan Wiggins Adire Audio 
26th May 2004, 06:16 PM  #3 
diyAudio Member
Join Date: Aug 2003
Location: Quebec city

Thanks Dan,
I wonder, I saw the parthenon driver used as a dipole driver. How come the front pressure wave and rear pressure wave don't cancel each other? F 
26th May 2004, 07:19 PM  #4 
diyAudio Member
Join Date: Jan 2004
Location: Toronto, ON, Canada

They do if the Parthenon isn't put into an enclosure.

26th May 2004, 08:30 PM  #5  
diyAudio Member
Join Date: Feb 2004
Location: Stockholm

Re: SPL function of speed or acceleration
Quote:
If mounted in a box it is proportional to the acceleration. The pressure from a point source is: p=(U*rho0*w)/(4*pi*r) where U is the volume flow (m3/s), rho0 is the density of air (=1.2 m3/s), w is the angular frequency (rad/s), r is the distance. Free field conditions are assumed. For low frequencies, a loudspeaker can be approcimated by a point source, and volume flow U is: U=Sd*v where Sd is the equivalent piston area of the speaker, and v is the velocity of the cone. So p is oproportional to w*v which in turn is equal to the acceleration (with a 90 degree phase shift). 

26th May 2004, 10:18 PM  #6  
diyAudio Member
Join Date: Aug 2002
Location: Seattle or Shanghai

Quote:
The concept was not only to make the wildest looking driver you've ever seen, but one with so much potential output that it's kind of a "so what" in terms of loss. There's so much to start with, you don't NEED a box. Dan Wiggins Adire Audio 

26th May 2004, 10:32 PM  #7 
diyAudio Member
Join Date: Apr 2004
Location: Texas

Based on your equations, it appears, then, that a more efficient or louder speaker of equal Sd would have a better transient response. Is this correct?

27th May 2004, 04:32 AM  #8 
diyAudio Member

is there a video of that thing going at it?
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27th May 2004, 06:26 AM  #9  
diyAudio Moderator Emeritus
Join Date: Jan 2002
Location: Michigan

Re: SPL function of speed or acceleration
Quote:
Sound pressure is proportional to the cone velocity. Two examples, one real and one conceptual. 1.) A jet plane has broken the sound barrier and is now traveling at a constant speed of mach 1.X. The "sonic boom" is a sonic pressure wave created by the plane traveling at a contasnt velocity. The planes acceleration is zero. 2.) A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly. The cone moves at a constant velocity and changes direction instantaneously at the ends of its travel. Sound pressure will be generated by the movement of the cone and the SPL will be proportional to the cones velocity. If the SPL were proportional to the acceleration, the SPL would be infinite.
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Rodd Yamashita 

27th May 2004, 08:50 AM  #10  
diyAudio Member
Join Date: Nov 2003
Location: Brighton UK

Quote:
A bit like amplifier slew rate requirements  which is faster : a) a 10W 10V/us amplifier or b) a 100W 20V/us amplifier ? some would say b) by definition, but IMO its a). sreten. 

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